The idea of sentence depth of Yngve (A Model and an Hypothesis for Language Structure, Proc. Am. Phil. Soc., Vol. 104, No. 5, Oct. 1960) is extended to the notion of “distance” between constituents of a construction. The distance between constituents is defined as a weighted sum of the number of IC cuts separating them. Yngve’s depth is then a maximum distance from a sentence to any of its words. Various systems of weighting cuts are investigated. For example, in endocentric structures we may require that the distance from an attribute to the structure exceeds the distance from the head to the structure, and in exocentric structures that the distances from each constituent to the structure are equal. Representations of constructions are considered which preserve the distance between constituents. It is shown that it is impossible to represent some sentences in Euclidean space with exact distances, but a representation may be found if only relative order is preserved. If more general spaces are used then exact distances may be represented. It follows that for a wide class of sentence types, there is a weighting, and a space, in which the distance preserving representations are identical with the diagrams of traditional grammar.